Question

The average of first 20 multiples of 9 will be

Answer 1

Answer:

94.5

Step-by-step explanation:

the middle place of first 20 multiples of 9 are 90 and 99

so,

n(1)+n(2)/2

90+99/2

=94.5

Answer 2

The average of first 20 multiples of 9 is 94.5

Step-by-step explanation:

To find: The average of first 20 multiples of 9

Now first 20 multiples of 9 are

9, 18, 27, 36 ,................

Therefore the difference between two consecutive terms are equal therefore it forms an A.P.

Now as we know sum of n terms of an A.P. is given by

$S_n=\dfrac{n}{2} (2a+(n-11)d)$

where a is the first term and d is the common difference

Now first term ;a= 9 and common difference;d = 18-9 = 9

So the sum of 20 terms of A.P. is

$S_{20}= \dfrac{20}{2} (2\times 9+(20-1) 9)\\\\\Rightarrow S_{20} =10(18+19\times9)= 1890$

Now average is given by

$average= \dfrac{\text {Sum of observations}}{\text {Number of observations}} =\dfrac{1890}{20} =94.5$

Hence the average of first 20 multiples of 9 is 94.5

#Learn  more

Find the mean of first 10 multiple of 7

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